Interpretation of torsional shear results for nonlinear stress-strain relationship

Torsional tests are frequently used in material testing to determine shear stress-strain relationships. In the tests, torque is applied to a solid or hollow cylindrical specimen, whose twist angle is recorded as the response. While the raw test results are readily available in terms of torque-twist sets, converting them into intrinsic stress-strain relationships is not always straightforward, owing to the nonlinear stress-strain behavior and the non-uniform radial distribution of the stress and strain fields. It follows that the approaches currently used to interpret torsional data are essentially empirical based. The present paper addresses this data interpretation issue from a more rigorous perspective. The paper includes two parts: the first part concerns hollow cylindrical specimens under torsion, where an analytical-based recursive procedure is developed; and the second part deals with solid torsional specimens, for which an analytical solution given by Nadai is directly employed. Examples pertaining to these two cases are examined and the resulting shear stress-strain curves are compared with those based on a number of popular empirical methods. The proposed analytical approaches can serve as a benchmark for checking the accuracy and validity of those empirical propositions. It is worth noting that, for brittle materials exhibiting softening behavior, only the analytical method gives the correct interpretation. Copyright (c) 2007 John Wiley & Sons, Ltd